Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time

Michele Bonollo, Luca Di Persio, Luca Mammi and Immacolata Oliva

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Abstract: In recent years, the counterparty credit risk measure, namely the default risk in \emph{Over The Counter} (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of \emph{Basel II} and \emph{Basel III.} More explicitly, to obtain the related risk figures, one has first obliged to compute intermediate output functionals related to the \emph{Mark-to-Market} (MtM) position at a given time $t \in [0, T],$ T being a positive, and finite, time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value.

Date: 2017-04
New Economics Papers: this item is included in nep-rmg
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